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Math Help - The function is defined if...

  1. #1
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    The function is defined if...

    (e^( cos^(-1) (log x^2) ))^1/2

    The base of log is 4
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  2. #2
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    Quote Originally Posted by utsav View Post
    (e^( cos^(-1) (log x^2) ))^1/2

    The base of log is 4
    What are you trying to do?
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    Quote Originally Posted by Prove It View Post
    What are you trying to do?
    The question is: The function is defined if..., we have to find the domain of the given function.
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    Quote Originally Posted by utsav View Post
    (e^( cos^(-1) (log x^2) ))^1/2

    The base of log is 4
    f(x) = \sqrt{e^{\arccos{[\log{(x^2)}]}}}.


    Note that the logarithm is only defined for x > 0.

    Since x^2 \geq 0, we can already see that we can not let x = 0.

    Also note that \arccos{x} is only defined for -1 \leq x \leq 1.

    The exponential function is always >0, so there are not any further restrictions for the square root.


    Thus the domain is x \in [-1, 0)\cup(0, 1].
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